The evolution of strained Ge/Si(001) islands during exposure to a Si flux was investigated by scanning tunneling microscopy. Dome islands display appreciable shape changes at Si coverages as low as 0.5 monolayer. With increasing coverage, they transform into -faceted pyramids, and eventually into stepped mounds with steps parallel to the <110> directions. These morphological changes are induced by alloying and represent a complete reversal of those previously observed during Ge island growth. The results are interpreted with a simple model in which the equilibrium shape of an island mainly depends on its volume and composition.